Time Optimal Path-Tracking Control of Kinematically Redundant Manipulators

Abstract

In this study, we propose a time optimal control scheme for kinematically redundant manipulators to track a predefined geometric path, subject to joint torque limits. The scheme can make full use of redundancy to increase the path-tracking velocity, and the time optimal trajectory planning problem is solved by using the phase-plane analysis and the linear programming technique. Computer simulation is also executed on a three-link planar rotary manipulator to show that, 1) the redundancy of the manipulator is fully used to increase the path-tracking velocity, and 2) redundant joints plus one more joint use their bound values of torque all the time while the time optimal path-tracking task is performed.

An explicit approach for time‐optimal trajectory planning for kinematically redundant serial robots

“…In order to exploit a manipulator's kinematic redundancy, internal motion in the Jacobian null space [2] is added according to certain performance criteria such as kinematic [3] or dynamic [4] manipulability. In [1] a method for obtaining minimum-time trajectories along predefined, parameterized task space paths of kinematically redundant serial robots is presented. The joint space is decomposed by separating m arbitrarily chosen joint coordinates yielding a non-redundant set of m joints and a redundant set of (n − m) coordinates.…”

“…The resulting trajectories are only C 1 continuous, which limits the method's range of possible applications. The present contribution adapts the joint space decomposition approach from [1]. A closed-form solution for the non-redundant joint coordinates q nr can be computed from the current position of the redundant joints q r and the geometric end-effector position along the prescribed path z E (s) where s denotes a scalar path coordinate and s (t) ∈ [0, 1] , s (0) = 0, s (t E ) = 1, i.e.…”

Efficient motion planning for fast motion of path tracking task with constant hand speed using redundant manipulator

“…The response of q q q is measured, and the responses ofq q q andq q q are estimated by observer. After that, the responses of R x , R v , and R a are calculated using (5), (6), and (7). The responses of redundancy are compared with references of redundancy in order to verify the relation between R x , R v , and R a .…”

“…2) A method of considering placement problem of hand path can realize by using indexes that indicate performance of manipulator on each hand position and posture [3], [4], [5], [6]. 3) A method of use subtask execution ability of redundant manipulators has been proposed time optimal path tracking control for redundant manipulator [7], [8], and a method to optimize joint torque and joint velocity [9], [10].…”

Redundancy Resolution in Minimum-time Path Tracking of Robotic Manipulators

“…There are various joint space decomposition approaches, some have drawbacks such as the inability to process certain paths, or boundary conditions, c.f. (Ma and Watanabe, 2004). Others rely on diffeomorphisms that may be difficult to obtain, c.f.…”